Moving Charge in a Magnetic Field question from NEET 2001 (AIPMT)

Answer: (c)

1. Magnetic force gives the centripetal force: $evB = \dfrac{mv^2}{r} \Rightarrow \omega = \dfrac{v}{r} = \dfrac{eB}{m}$.
2. Frequency $f = \dfrac{\omega}{2\pi} = \dfrac{eB}{2\pi m}$, independent of $E$.
3. So the answer is (c) $\frac{eB}{2\pi m}$.